The present invention relates generally to a method and system for determining the relative positions between two or more locations, such as survey marks, using radio signals broadcast by the Global Positioning System ("GPS") satellites of the United States and the Global Satellite Navigation System ("GLONASS") satellites of the former USSR, and more particularly to improved methods of signal processing and instrumentation for determining these positions.
There are many GPS and GLONASS applications being implemented, both military and commercial. An appropriate receiver in an aircraft, ship, tractor, automobile, or the like, allows a user to determine position and/or velocity. Another application is surveying to accurately determine the location of a point or a distance between two or more points. It is this last application to which the present invention most closely pertains.
As is well known, GPS was established by the United States government, and employs a constellation of satellites in orbit around the earth at an altitude of approximately 26500 km. Currently, the GPS constellation consists of 24 satellites, arranged with 4 satellites in each of 6 orbital planes. Each orbital plane is inclined to the earth's equator by an angle of approximately 55 degrees.
Each GPS satellite transmits microwave L-band radio signals continuously in two frequency bands, centered at 1575.42 MHz and 1227.6 MHz., denoted as L1 and L2 respectively. The GPS L1 signal is quadri-phase modulated by a coarse/acquisition code ("C/A code") and a precision ranging code ("P-code"). The L2 signal is binary phase shift key ("BPSK") modulated by the P-code. The GPS C/A code is a gold code that is specific to each satellite, and has a symbol rate of 1.023 MHz. The unique content of each satellite's C/A code is used to identify the source of a received signal. The P-code is also specific to each satellite and has a symbol rate of 10.23 MHz. The GPS satellite transmission standards are set forth in detail by the Interface Control Document GPS (200), dated 1993, a revised version of a document first published in 1983.
GLONASS was established by the former Soviet Union and operated by the Russian Space Forces. The GLONASS constellation consists of 24 satellites arranged with 8 satellites in each of 3 orbital planes. Each orbital plane is inclined to the earth's equator by an angle of approximately 64.8 degrees. The altitude of the GLONASS satellites is approximately 19100 km.
The satellites of the GLONASS radio navigation system transmit signals in the frequency band near 1602 MHz, and signals in a secondary band near 1246 MHz, denoted as L1 and L2 respectively. The GLONASS L1 signal is quadri-phase modulated by a C/A code and a P-code. The L2 signal is BPSK modulated by the P-code. Unlike GPS, in which all of the satellites transmit on the same nominal frequency, the GLONASS satellites each transmit at a unique frequency in order to differentiate between the satellites. The GLONASS L1 carrier frequency is equal to 1602 MHz+k * 0.5625 MHz, where k is a number related to the satellite number. The GLONASS L2 carrier frequency is equal to 1246 MHz+k * 0.5625 MHz. The GLONASS C/A code consists of a length 511 linear maximal sequence. Details of the GLONASS signals may be found in the Global Satellite Navigation System GLONASS-Interface Control Document of the RTCA Paper No. 518-91/SC159-317, approved by the Glavkosmos Institute of Space Device Engineering, the official former USSR GLONASS responsible organization.
Although no carriers are present in the transmitted GPS and GLONASS signals, the carriers may be said to be implicit therein. The term "carrier" refers to a component having an effectively constant amplitude and phase. Because the GPS and GLONASS signals are modulated by pseudorandom codes, on average, the band center frequency carrier is suppressed. The term "carrier" is used herein refers to the dominant spectral component after the modulation is removed.
The carrier is reconstructed in a GPS or a GLONASS receiver by one of a number of techniques. The most straight forward technique is to multiply the received signal with a locally generated estimate of the modulation contained on the received signal. The P-code of GPS satellites, however, is usually encrypted, the encrypted precision ranging code being termed a "Y-code". The purpose of encrypting the P-code is to prevent "spoofing," which is the possibility of a hostile force emulating a GPS satellite signal to cause military airplanes, ships and the like to be misdirected and calculate incorrect values of velocity, position, time and the like. There are, however, methods utilized to recover the carrier from the encrypted signals and provide an estimate the P-code without decryption being necessary, such as the methods described in U.S. Pat. No. 5,134,407, Lorenz et al., that are useful for surveying and other commercial applications.
None of the GLONASS signals are encrypted but the P-code has not been officially published. However, the GLONASS P-code has been determined to be derived from a length 2**25-1 linear maximal sequence. [Lennen, Gary R., "The USSR's GLONASS P-Code Determination and Initial Results", ION GPS-89, Colorado Springs, Sep. 27-29, 1989]. The inventors have verified the results of Lennen and have found them to be correct. There has been no assurance that this code will not be changed in the future.
There are many factors that affect the accuracy of measurements made through either GPS or GLONASS. The path of travel, or ephemeris, of each satellite is elliptical and subject to being altered by solar winds and other natural causes. Since the accuracy of any measurement is dependent upon knowledge of the position of the involved satellites at any given time, an estimate of the path of travel is calculated on earth for each of the satellites and periodically uploaded into it. The estimated position of each satellite is then part of the data that is transmitted as part of its signals that are used by a receiver on earth. Other causes of inaccuracies include variable effects of the ionosphere and troposphere on propagation of signals from the satellites to the receivers.
The accuracy of the GPS system is also intentionally degraded in order to limit its usefulness to users not authorized by the United States military. The intentional degradation is introduced through controlled variation of the satellite clocks and ephemeris data. The relative phases of signals transmitted by all the GPS satellites are periodically shifted by simultaneously dithering the internal clocks of the satellites. The resulting condition is generally referred to as Selective Availability ("SA"). The accuracy of GPS for the United States military is not affected, since military users are provided with cryptographic methods to remove the introduced satellite clock and ephemeris data errors. GLONASS has no such intentional accuracy degradation. When using GPS to determine the relative position between two stations, the SA induced errors are common to both stations and approximately cancel.
The use of GPS in commercial applications, such as surveying, is quite valuable and rapidly increasing. Since the GPS satellite positions are known, a point on earth may be geometrically determined by simultaneously measuring the range from that point to three satellites. This is, basically, a standard trilateration technique. The range to each of the three satellites can be viewed as the radius of a spherical surface having the satellite at its center. The point of intersection of all three spherical surfaces is the point whose position is being determined. In GPS, the positions of the satellites and locations on earth are expressed as vectors in a coordinate system with an (x,y,z) position of (0,0,0) located at the center of the earth.
The range from a receiver to a satellite is determined by measuring, in effect, the time that it takes for the signal to traverse from the satellite to the receiver, with knowledge of the position of the satellite. Each of the satellites have internal clocks that are synchronized to a single GPS time. The receiver has a clock which is not, in general, synchronized to GPS time. Thus, the ranges to four or more satellites are simultaneously measured in order to be able to solve for four unknowns, namely the three spatial coordinates of the receiver location and an offset of the receiver clock time from the GPS time.
Some GPS receivers use the C/A code carried by the L1 signal, providing range measurements that are not particularly precise (typically about one meter) because of the relatively low repetition rate of the C/A code. This technique is used in inexpensive position receivers, where the accuracy provided by this technique is quite adequate. These receivers lock onto the C/A code by correlating the received signals with an internally generated replica of the C/A code. Other receivers use the P-code, which increases the accuracy because of the higher repetition rate, but requires that the P-code be known or estimated so that it can be generated within the receiver in order to be correlated with the incoming signal. The most accurate results are obtained, however, by receivers that use the carrier signal reconstructed from the satellite signals for making range measurements. The present invention makes use of the reconstructed carrier to make accurate relative position measurements.
Techniques for determining the relative positions of two spaced apart points using GPS are well known. In the usual GPS receiver signal processing technique, the range to a satellite is expressed in terms of an integer N, which represents a number of whole cycles of the carrier between the earth location and the satellite, as adjusted by terms representing a fractional portion of a carrier cycle (a phase term .phi.) and offsets of the receiver and satellite clocks from true GPS time (a clock bias .delta.). A given measurement includes acquiring signals from multiple satellites at the same time (during a first epoch t) in order to produce data from which multiple equations with multiple variables may be solved for the desired ranges. Signals are usually again acquired during a second epoch (t+1), and others, in order to improve the signal-to-noise ratio of the received signal. In applications where the distance between two points is being measured, the application with which the present invention specifically pertains, well known GPS signal processing techniques exist.
Several papers discuss the use of GPS and GLONASS carrier phase relative positioning, as follows:
1) "The GG24 Combined GPS+GLONASS Receiver", S. Gourevitch, S. Sila-Novitsky, F. van Diggelen, Proceedings of ION-GPS '96, September 17-20, Kansas City, Mo. PA1 2) "Test Results from a New 2 cm Real Time Kinematic GPS Positioning System", J. B. Neumann, A. Manz, T. J. Ford, O. Mulyk, Proceedings of ION-GPS '96, September 17-20, Kansas City, Mo. PA1 3) "GPS and GLONASS Carrier Phase Ambiguity Resolution", D. Walsh, P. Daly, Proceedings of ION-GPS '96, September 17-20, Kansas City, Mo. PA1 4) "Carrier Phase Ambiguity Resolution using GPS and GLONASS signals", H. Landau, U.Vollath, Proceedings of ION-GPS '96, September 17-20, Kansas City, Mo. PA1 5) "Ashtech RTZ, Real-Time Kinematic GPS with OTF Initialization", S. Gourevitch, F. van Diggelen, X. Qin, M. Kuhl, Proceedings of ION-GPS '95, September 12-15, Palm Spring, Calif. PA1 6) "On Maximum Likelihood Estimate in Multi-Scale Measurement Device", A. Povalyaev, Raditekhnika i Electronika, v.21, No.5, 1976. Simultaneous English translation of the Journal of Communication Technology and Electronic ISSN 1064-2269. PA1 7) Calculation of Quality Characteristics and Synthesis of Multiscale Measuring Devices Which Generate Maximum Likelihood Estimates, A. Povalyaev, Raditekhnika i Electronika, v.23, No.1, 1978. Simultaneous English translation of the Journal of Communication Technology and Electronic ISSN 1064-2269. PA1 8) Counselman and Gourevitch, "Miniature Interferometer Terminals for Earth Surveying: Ambiguity and Multipath with Global Positioning System," IEEE Transactions on Geoscience and Remote Sensing, GE-19, pp. 244-252 (1981); PA1 9) Counselman, Abbot, Gourevitch, King and Paradis, "Centimeter-Level Relative Positioning with GPS," Journal of Surveying Engineering," 109, pp. 81-89 (1983); PA1 10) Bock, Abbot, Counselman, Gourevitch, King and Paradis, "Geodetic Accuracy of the Macrometer Model V-1000," Bulletin Geodesique, 58, pp. 211-221 (1984); PA1 11) Bock, Abbot, Counselman, Gourevitch and King, "Establishment of a Three-Dimensional Geodetic Control Network by Interferometry with the Global Positioning System, Journal of Geophysical Research, 90, B9, pp. 7689-7703 (1985); PA1 12) Bock, Gourevitch, Counselman, King and Abbot, "Interferometric Analysis of GPS Phase Observations," Man. Geod., 11, pp. 282-288 (1986); and PA1 13) Abbot, Counselman, Gourevitch and Ladd, "GPS Orbit Determination: Bootstrapping to Resolve Carrier Phase Ambiguity," Proc. Of the Fifth International Geodetic Symposium on Satellite Positioning, Las Cruces, N. Mex. (Mar. 13-17, 1989).
Several papers discuss the theory of ambiguity resolution, as follows:
Several early papers discuss range measuring techniques and theory, as follows:
A book by Hofmann-Wellenhof, Lichtenegger and Collins, GPS Theory and Practice, Third edition, Springer-Verlag, 1994, also discusses GPS relative position measurements. It is the mathematical notation in this book that is attempted to be followed herein. Section 8.2, entitled "Relative Positioning" at pages 183-197, and sections 9.1-9.3 of the Data Processing chapter, pages 199-244, are particularly pertinent to the present invention. This book is hereby incorporated into this Background by this reference.
Briefly, the processing of GPS signals for determining the location of two points along a baseline is accomplished by forming single differences of the range equations of the two points with respect to each of the satellites during a single epoch, combining ambiguity and clock bias terms N and .delta., respectively, and then forming double difference equations from a difference between two single difference equations relating to two different satellites. In this combining, the clock bias terms drop out because the carrier frequencies of each of the GPS satellites are the same.
The use of GLONASS approximately doubles the number of available navigation space vehicles (SVs) compared to GPS only operation. There are also additional advantages for civilian users. It has already been proved that tracking both GPS and GLONASS signals yields substantially improved stand alone position accuracy [see reference 1, above], since GLONASS has no Selective Availability type of degradation. For code differential processing, combining GPS with GLONASS provides a significant benefit. One of the most significant aspects of any real-time kinematic processing which makes use of differential code and carrier data, is the speed and reliability of the on-the-fly ambiguity resolution, i.e., the ability of the processing to determine the integer number of unknown cycles present in the differential carrier measurement. The ability to resolve the integer ambiguities affords the user with centimeter level accuracy as well as a confidence in the accuracy of these measurements. With GPS-only, in order to get fast on-the-fly ambiguity resolution, there is a need to use the L2 frequency and hence expensive P code receivers [reference 2, above]. While for many applications it is desirable to track the L1 and L2 signals from GPS and GLONASS, in cost sensitive applications it may be of advantage to use only the L1 frequencies of GPS and GLONASS.
Combined GPS plus GLONASS differential processing involves more than adding extra GLONASS codes and carriers to standard GPS RTK engine. The main problems arise from the fact that GLONASS has different frequencies for different SVs. Some authors [references 3 and 4, above] report that inter-channel hardware biases may make ambiguity resolution for GLONASS impossible without preliminary receiver calibration. There are also some additional difficulties in such a process which will be discussed later.
The difference in frequencies of the individual GLONASS satellites precludes the use of the above summarized carrier phase processing technique. The terms of the equations which represent receiver clock biases do not automatically drop out as they do when processing GPS signals. As a result, GLONASS processing uses code phases, not carrier phases, and the results are not as accurate as with the GPS system.
Therefore, it is a primary object of the present invention to provide combined GPS plus GLONASS satellite receiver signal processing techniques that provide the same accuracy of relative positioning measurements as current GPS signal processing techniques but afford much improved capability to resolve integer ambiguities which results in accuracy as well as reliability of said solution.
It is another object of the present invention to provide such techniques that are useable without regard for whether an individual satellite signal being processed originates in a GPS or GLONASS satellite.
It is another object of the present invention to provide an improved satellite signal processing method and receiver apparatus for determining the relative positions of two points.